Question 583309
Area = base*height
{{{ 52 = h*( 2h + 5 ) }}}
{{{ 52 = 2h^2 + 5h }}}
{{{ 2h^2 + 5h -52 = 0 }}}
Use the quadratic formula
{{{h = ( -b +- sqrt( b^2 - 4*a*c ))/(2*a) }}}
{{{ a = 2 }}}
{{{ b = 5 }}}
{{{ c = -52 }}}
{{{h = ( -5 +- sqrt( 5^2 - 4*2*(-52) ))/(2*2) }}}
{{{h = ( -5 +- sqrt( 25 + 416 )) / 4 }}}
{{{h = ( -5 +- sqrt( 441 )) / 4 }}}
{{{h = ( -5 +- 21 ) / 4 }}} ( ignore the negative square root )
{{{ h = ( -5 + 21 ) / 4 }}}
{{{ h = 16/4 }}}
{{{ h = 4 }}}
The height is 4
check:
Area = {{{ h*( 2h + 5 ) }}}
Area = {{{ 4*( 2*4 + 5 ) }}}
Area = {{{ 4*13 }}}
Area = {{{ 52 }}}
OK